How to fully weight a mesh to a bone?
Yes. You can select Tab into Edit Mode, select one vertex of the shoulderMesh, FootMesh, etc. chunk, and key Ctrl + L. If the chunks really are separate, this should select only one chunk. If they are not truly separate, Box or otherwise select the chunk.

With the chunk selected, go to the Properties panel > Object Data tab > Vertex Groups panel. Find the corresponding Vertex Group (should be named after your bone), make sure the Weight: value is set to 1, and click Assign.

One Vertex Selected:



Ctrl + L keyed to select entire chunk:



Vertex Groups panel. Assign button visible while still in Edit Mode. Weight at 1 guarantees maximum weight assigned: